Generalized Kähler-Einstein metric along Q-Fano fibration

Jolany, Hassan

Document type :

Pré-publication ou Document de travail

Title :

Generalized Kähler-Einstein metric along Q-Fano fibration

Author(s) :

Jolany, Hassan [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

In this paper, we show that along $\mathbb Q$-Fano fibration, when general fibres, base and central fiber (with at worst Kawamata log terminal singularities)are K-poly stable then there exists a relative K\"ahler-Einstein ...
Show more >In this paper, we show that along $\mathbb Q$-Fano fibration, when general fibres, base and central fiber (with at worst Kawamata log terminal singularities)are K-poly stable then there exists a relative K\"ahler-Einstein metric. We introduce the fiberwise K\"ahler-Einstein foliation and we mention that the main difficulty to obtain higher estimates is to solve relative CMA equation along such foliation. We propose a program such that for finding a pair of canonical metric $(\omega_X,\omega_B)$, which satisfies in $Ric(\omega_X)=\pi^*\omega_B+\pi^*(\omega_{WP})+[\mathcal N]$on K-poly stable degeneration $\pi:X\to B$, where $Ric(\omega_B)=\omega_B$, we need to have Canonical bundle formula.Show less >

Language :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

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